Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T09:27:42.299Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL ADMISSION CONTROL IN QUEUES WITH WORKLOAD-DEPENDENT SERVICE RATES

Published online by Cambridge University Press:  19 September 2006

René Bekker  and
Sem C. Borst
René Bekker
Affiliation:
Vrije Universiteit, Amsterdam, 1081 HV Amsterdam, The Netherlands, E-mail: [email protected]
Sem C. Borst
Affiliation:
Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, and, CWI, 1090 GB Amsterdam, The Netherlands, and, Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a queuing system with a workload-dependent service rate. We specifically assume that the service rate is first increasing and then decreasing as a function of the amount of work. The latter qualitative behavior is quite common in practical situations, such as production systems. The admission of work into the system is controlled by a policy for accepting or rejecting jobs, depending on the state of the system. We seek an admission control policy that maximizes the long-run throughput. Under certain conditions, we show that a threshold policy is optimal, and we derive a criterion for determining the optimal threshold value.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 543 - 570
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bekker, R. (2005). Finite-buffer queues with workload-dependent service and arrival rates. Queueing Systems 50: 231–253.Google Scholar
Bekker, R., Borst, S.C., Boxma, O.J., & Kella, O. (2004). Queues with workload-dependent arrival and service rates. Queueing Systems 46: 537–556.Google Scholar
Bertrand, J.W.M. & van Ooijen, H.P.G. (2002). Workload based order release and productivity: A missing link. Production Planning & Control 13: 665–678.Google Scholar
Cohen, J.W. (1976). On regenerative processes in queueing theory. Lecture Notes in Economics and Mathematical Systems Vol. 121. Berlin: Springer-Verlag.
Cohen, J.W. (1976). On the optimal switching level for an M/G/1 queueing system. Stochastic Processes and Their Applications 4: 297–316.Google Scholar
Doshi, B.T. (1974). Continuous time control of Markov processes on an arbitrary state space. Ph.D. thesis, Cornell University, Ithaca, NY.
Doshi, B.T. (1977). Continuous time control of the arrival process in an M/G/1 queue. Stochastic Processes and Their Applications 5: 265–284.Google Scholar
Feinberg, E.A. & Kella, O. (2002). Optimality of D-policies for an M/G/1 queue with a removable server. Queueing Systems 42: 355–376.Google Scholar
Harrison, J.M. & Resnick, S.I. (1976). The stationary distribution and first exit probabilities of a storage process with general release rule. Mathematics of Operations Research 1: 347–358.Google Scholar
Van Ooijen, H.P.G. & Bertrand, J.W.M. (2003). The effects of a simple arrival rate control policy on throughput and work-in-process in production systems with workload dependent processing rates. International Journal of Production Economics 85: 61–68.Google Scholar
Ritt, R.K. & Sennott, L.I. (1992). Optimal stationary policies in general state space Markov decision chains with finite action sets. Mathematics of Operations Research 17: 901–909.Google Scholar
Ross, S.M. (1968). Arbitrary state Markov decision processes. Annals of Mathematical Statistics 39: 2118–2122.Google Scholar
Ross, S.M. (1970). Average cost semi-Markov decision processes. Journal of Applied Probability 7: 649–656.Google Scholar
Schäl, M. (1993). Average optimality in dynamic programming with general state space. Mathematics of Operations Research 18: 163–172.Google Scholar
Tijms, H.C. (1976). Optimal control of the workload in an M/G/1 queueing system with removable server. Mathematische Operationsforschung und Statistik 7: 933–944.Google Scholar